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प्रश्न
Given A = {x : ∈ N :< 6}, B = {3, 6, 9} and C {x ∈ N : 2x - 5 ≤ 8}. show that: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
उत्तर
A = {x : ∈ N :< 6}
B = {3, 6, 9}
C = {x ∈ N : 2x - 5 ≤ 8}
2x - 5 ≤ 8
⇒ 2x ≤ 8+5
⇒ 2x ≤ 13
⇒ x ≤ `13/2`
⇒ x ≤ 6.5
∴ C = {1, 2, 3, 4, 5, 6}
B ∪ C = {3, 6, 9} ∪ {1, 2, 3, 4, 5, 6}
= {1, 2, 3, 4, 5, 6, 9}
A ∩ (B ∪ C) = {1, 2, 3, 4, 5} ∩ {1, 2, 3, 4, 5, 6, 9}
= {1, 2, 3, 4, 5}
Now A ∩ C = {1, 2, 3, 4, 5} ∩ {1, 2, 3, 4, 5, 6}
= {1, 2, 3, 4, 5}
A ∩ B = {1, 2, 3, 4, 5} ∩ {3, 6, 9}
= {3}
∴ (A ∩ B) ∪ (A ∩ C) = {3} ∪ {1, 2, 3, 4, 5}
= {1, 2, 3, 4, 5}
∴ A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
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